On the proof theory of the modal logic for arithmetic provability

DOI10.2307/2273755zbMath0464.03019OpenAlexW2036161385MaRDI QIDQ3914957

Daniel Leivant

Publication date: 1981

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2273755

zbMATH Keywords

cut eliminationprovabilityinterpolation theoremcut free derivationsquantifier extensions

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) Cut-elimination and normal-form theorems (03F05)

Related Items (16)

VALENTINI’S CUT-ELIMINATION FOR PROVABILITY LOGIC RESOLVED ⋮ Provability multilattice logic ⋮ On the proof-theory of two formalisations of modal first-order logic ⋮ A realization theorem for the Gödel-Löb provability logic ⋮ 2003 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquim '03 ⋮ Machine Checking Proof Theory: An Application of Logic to Logic ⋮ A cut-free sequential system for the propositional modal logic of finite chains ⋮ Unnamed Item ⋮ The Closed Fragment of IL is PSPACE Hard ⋮ A PURELY SYNTACTIC AND CUT-FREE SEQUENT CALCULUS FOR THE MODAL LOGIC OF PROVABILITY ⋮ The modal logic of provability: cut-elimination ⋮ The modal logic of provability. The sequential approach ⋮ Modal tableau calculi and interpolation ⋮ On some proof theoretical properties of the modal logic GL ⋮ Circular proofs for the Gödel-Löb provability logic ⋮ Proof analysis in modal logic

Cites Work

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• Provability interpretations of modal logic
• Failures of the interpolation lemma in quantified modal logic
• Solution of a problem of Leon Henkin
• Reflection principles and iterated consistency assertions

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